The guitar amp plugins don't generate any noise; they only process the sound that you send into them. Distortion and guitar amp plugins frequently have this problem where they seem to add hiss, but in fact, this is just the nature of distortion. It brings up the noise that you send into it. It might seem like the signal from your DI box is quiet, but there can be all kinds of noise hiding in there.
There are a few things you can do to reduce the noise when using guitar amp plugins like this. First, use active guitar pickups if possible, and use new, quality cables. If your DI box has a "cabinet sim," turn it off. Also make sure that the signal that you're sending into the plugin is as loud as possible, without clipping. Also, in the plugin, bring the gain down as much as you can without losing the distortion that you want, and then bring the output level up to compensate.